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We study series of the form $\sum_{M} | {Aut}_{R} {(M) |}^{- 1} {| M |}^{- u}$ , where $R$ is a commutative local ring, $u$ is a non-negative integer, and the summation extends over all finite $R$ -modules $M$ , up to isomorphism. This problem is motivated by Cohen-Lenstra heuristics on class groups of number fields, where sums of this kind occur. If $R$ has additional properties, we will relate the above sum to a limit of zeta functions of the free modules $R^{n}$ , where these zeta functions count $R$ -submodules of finite index in $R^{n}$ . In particular we will show that...

Cohen-Macaulay and Gorenstein finitely graded rings

Claudia Menini (1988)

Rendiconti del Seminario Matematico della Università di Padova

Cohen-Macaulay and Gorenstein property of rees algebras of non-singular equimultiple prime ideals.

Ngo Viet Trung, Duong Quoc Viet (1992)

Manuscripta mathematica

Cohen-Macaulay Properties in the Koszul Homology.

Herbert Sanders (1986)

Manuscripta mathematica

Cohen-Macaulay-Punkte auf lokal geringten Räumen und Anwendungen in der Schnittheorie

M. HERRMANN, W. VOOEL (1974)

Beiträge zur Algebra und Geometrie = Contributions to algebra and geometry

Commutative n-Gorenstein Rings.

Idun Reiten, Robert Fossum (1972)

Mathematica Scandinavica

Complete intersection augmented algebras.

S. Zarzuela (1996)

Mathematische Annalen

Complete local factorial rings which are not Cohen-Macaulay in characteristic $p$

Robert M. Fossum, Phillip A. Griffith (1975)

Annales scientifiques de l'École Normale Supérieure

Condition $G_{q}$ d’Ischebeck-Auslander et condition $S_{q}$ de Serre

Michel Paugam (1972/1973)

Séminaire Dubreil. Algèbre et théorie des nombres

Copure injective resolutions, flat resolvents and dimensions

Edgar E. Enochs, Jenda M. G. Overtoun (1993)

Commentationes Mathematicae Universitatis Carolinae

In this paper, we show the existence of copure injective preenvelopes over noetherian rings and copure flat preenvelopes over commutative artinian rings. We use this to characterize $n$ -Gorenstein rings. As a consequence, if the full subcategory of strongly copure injective (respectively flat) modules over a left and right noetherian ring $R$ has cokernels (respectively kernels), then $R$ is $2$ -Gorenstein.

Currently displaying 1 – 20 of 20

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Displaying 1 – 20 of 20

Castelnuovo Bounds for Certain Subvarieties in IPn.

Castelnuovo's Regularity and Multiplicity.

Certain Complexes Associated to a Sequence and a Matrix.

Characterization of the Hilbert-Samuel polynomials of curve singularities

Characterizations of Buchsbaum Complexes.

Classification of the Tor-Algebras of Codimension Four Gorenstein Local Rings

Codimesion two linear varieties with nilpotent structures.

Cohen-Lenstra sums over local rings